Nonlinear Fokker–Planck–Landau integral propagator (II): transport far from equilibrium

Abstract

We present a time evolving path-integral method for solving the Landau–Fokker–Planck equation to compute kinetic transport coefficients in a fully ionized plasma. The electron distribution function is advanced in time by means of the conservative short-time propagators, which we previously obtained. The validated integral operator takes into account both electron–electron and electron–ion collisions without linearizing the original Fokker–Planck collisional operator. The resulting integral formulation in velocity space is applied here to evaluate the local transport coefficients if inhomogeneities in configuration space appear. We define an effective source term through a flux particle balance in a thin slab of plasma, which leads to a nonhomogeneous Fokker–Planck equation. Hence, this new term locally models the so-called Vlasov term appearing in the general kinetic equation. Arbitrary departures from Maxwellian equilibrium can be dealt with this effective source term that preserves the positiveness of the electron distribution function, even in the runaway limit. For small perturbations of the equilibrium, the classical Spitzer and Harm transport coefficients are recovered, while a very strong reduction of the heat flux takes place for large temperature gradients, as predicted by some authors in different theories.